Inking systems to which the present invention relates are known in the literature see, for example, the referenced German Disclosure Document No. DE-OS 2 052 806. As disclosed in this publication, measuring or metering rollers are provided which rotate with approximately the same surface speed as the ink transfer cylinder and the plate cylinder. Operating experience has shown that the uniformity and thickness or, rather, thinness of the film of ink applied by the system to the transfer cylinder can still be improved.